Embedding of hyperbolic spaces in the product of trees

Details Embedding of hyperbolic spaces in the product of trees Embedding of hyperbolic spaces in the product of trees

2003-11-28

arxiv.org/abs/math/0311524v1

Geom. Dedicata, 113 (2005), 75--93.

Mathematics

Geometric Topology

18 pages, 2 figures

Scientific paper

We show that for each n\ge 2 there is a quasi-isometric embedding of the
hyperbolic space H^n in the product T^n=Tx...xT of n copies of a (simplicial)
metric tree T. On the other hand, we prove that there is no quasi-isometric
embedding H^2 --> TxR^m for any metric tree T and any m\ge 0.

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